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38000

38000² = 1444000000 with 144 = 12² and 4000000 = 2000².

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38016

38016²± 5 are primes.

38016² = (2² - 1)(3² - 1)(5² - 1)(7² - 1)(10² - 1)(23² - 1) = (2² - 1)(5² - 1)(7² - 1)(10² - 1)(65² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38024

38024²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38025

38025 = 195², a square with different digits.

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

---

38070

38070² = (20² + 5)(29² + 5)(65² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38080

38080² = (3² - 1)(6² - 1)(33² - 1)(69² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38082

38082² = (1² + 2)(3² + 2)(8² + 2)(816² + 2) = (2² + 2)(19² + 2)(816² + 2)
= (3² + 2)(14² + 2)(816² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38090

38090² = (1² + 4)(3² + 4)(17² + 4)(276² + 4).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38106

38106² = (3² + 9)(7² + 9)(8² + 9)(138² + 9) = (3² + 9)(65² + 9)(138² + 9).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38132

38132² = 1454049424, a square pegged by 4.

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38199

38199²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38226

38226²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38250

38250² = (1² + 9)(3² + 9)(4² + 9)(12² + 9)(46² + 9) = (1² + 9)(4² + 9)(6² + 9)(12² + 9)(29² + 9)
= (1² + 9)(4² + 9)(21² + 9)(114² + 9) = (1² + 9)(6² + 9)(39² + 9)(46² + 9)
= (1² + 9)(12² + 9)(21² + 9)(46² + 9) = (3² + 9)(4² + 9)(5² + 9)(6² + 9)(46² + 9)
= (3² + 9)(4² + 9)(39² + 9)(46² + 9) = (3² + 9)(6² + 9)(29² + 9)(46² + 9)
= (3² + 9)(79² + 9)(114² + 9) = (4² + 9)(6² + 9)(29² + 9)(39² + 9)
= (4² + 9)(12² + 9)(21² + 9)(29² + 9) = (5² + 9)(6² + 9)(12² + 9)(79² + 9)
= (5² + 9)(6² + 9)(21² + 9)(46² + 9) = (12² + 9)(39² + 9)(79² + 9)
= (21² + 9)(39² + 9)(46² + 9).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38258

38258²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38304

38304² = (17² - 1)(20² - 1)(113² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38313

38313² = (1² + 2)(3² + 2)(59² + 2)(113² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38316

38316²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38325

38325² = (1² + 6)(3² + 6)(33² + 6)(113² + 6).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38358

38358² = (2² + 2)(4² + 2)(3691² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38367

38367² = (16² + 5)(32² + 5)(74² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38392

38392²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38400

38400² = (3² - 1)(9² - 1)(31² - 1)(49² - 1).

40³ + 38400 = 320², 40³ - 38400 = 160²,
200² + 38400 = 280², 200² - 38400 = 40².

Page of Squares : First Upload July 7, 2012 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38412

38412² = (2² + 8)(34² + 8)(325² + 8).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38416

38416 = 196²4

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38430

38430² = (1² + 5)(10² + 5)(19² + 5)(80² + 5) = (4² + 5)(5² + 5)(19² + 5)(80² + 5)
= (19² + 5)(25² + 5)(80² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38444

38444²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38448

38448² = (1² + 8)(2² + 8)(4² + 8)(9² + 8)(80² + 8) = (1² + 8)(2² + 8)(8² + 8)(436² + 8)
= (4² + 8)(8² + 8)(9² + 8)(98² + 8) = (4² + 8)(9² + 8)(10² + 8)(80² + 8)
= (4² + 8)(80² + 8)(98² + 8) = (8² + 8)(10² + 8)(436² + 8).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38454

38454² = (2² + 9)(7² + 9)(22² + 9)(63² + 9) = (5² + 9)(22² + 9)(297² + 9)
= (7² + 9)(63² + 9)(80² + 9).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38478

38478²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

---

38480

38480²± 3 are primes.

38480² = (1² + 4)(2² + 4)(10² + 4)(12² + 4)(49² + 4) = (1² + 4)(3² + 4)(6² + 4)(12² + 4)(62² + 4)
= (2² + 4)(3² + 4)(6² + 4)(12² + 4)(49² + 4) = (2² + 4)(3² + 4)(16² + 4)(234² + 4)
= (2² + 4)(4² + 4)(49² + 4)(62² + 4) = (3² + 4)(4² + 4)(10² + 4)(234² + 4)
= (3² + 4)(10² + 4)(12² + 4)(86² + 4) = (3² + 4)(12² + 4)(14² + 4)(62² + 4)
= (6² + 4)(10² + 4)(12² + 4)(49² + 4) = (10² + 4)(16² + 4)(234² + 4).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38487

38487²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38528

38528² = (1² + 7)(5² + 7)(6² + 7)(7² + 7)(49² + 7) = (1² + 7)(7² + 7)(37² + 7)(49² + 7)
= (5² + 7)(6² + 7)(21² + 7)(49² + 7) = (6² + 7)(7² + 7)(21² + 7)(37² + 7)
= (21² + 7)(37² + 7)(49² + 7).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38532

38532² = (6² + 3)(45² + 3)(137² + 3).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38544

38544² = (4² + 8)(6² + 8)(24² + 8)(49² + 8).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38546

38546²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38548

38548²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38551

38551² = 1059² + 1060² + 1061² + ... + 1780².

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38560

38560² = 27² + 29² + 31² + 33² + ... + 2073².

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38571

38571²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38639

38639 is the fourth prime for which the Legendre symbol (a/38639) = 1 for a = 1,2,..., 28.

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38640

38640² = (2² - 1)(3² - 1)(15² - 1)(22² - 1)(24² - 1) = (5² - 1)(15² - 1)(22² - 1)(24² - 1)
= (6² - 1)(47² - 1)(139² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38646

38646² = (1² + 2)(6² + 2)(26² + 2)(139² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38655

38655²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38656

38656² = (3² + 7)(5² + 7)(12² + 7)(139² + 7).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38672

38672²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38710

38710² = (1² + 6)(2² + 6)(22² + 6)(209² + 6) = (8² + 6)(22² + 6)(209² + 6).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38719

38719² = 159² + 161² + 163² + 165² + ... + 2079².

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38760

293² + 38760 = 353², 293² - 38760 = 217².

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38772

38772² = 15032679844

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38776

38776²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38836

38836² = (2² + 3)(17² + 3)(859² + 3).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38841

38841²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38868

29802² + 38868² = 2398880628, a mosaic square.

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38880

234² + 38880 = 306², 234² - 38880 = 126².

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38934

38934² = (1² + 5)(2² + 5)(11² + 5)(472² + 5) = (1² + 5)(4² + 5)(7² + 5)(472² + 5)
= (2² + 5)(3² + 5)(7² + 5)(472² + 5) = (7² + 5)(11² + 5)(472² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38961

38961² = 108⁴ + 135⁴ + 180⁴.

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012
by Yoshio Mimura, Kobe, Japan

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38982

38982²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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38994

38994² = (17² + 2)(20² + 2)(114² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

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